Probabilistic Structural Controllability in Causal Bayesian Networks
This addresses a foundational challenge in causal inference and decision-making under uncertainty, offering a theoretical framework for autonomy in uncertain environments, though it appears incremental as it builds on existing controllability concepts.
The paper tackles the problem of probabilistic controllability in Causal Bayesian Networks by formalizing it and identifying a sufficient set of driver variables to influence target variables, focusing on structural knowledge without requiring full parameter details.
Humans routinely confront the following key question which could be viewed as a probabilistic variant of the controllability problem: While faced with an uncertain environment governed by causal structures, how should they practice their autonomy by intervening on driver variables, in order to increase (or decrease) the probability of attaining their desired (or undesired) state for some target variable? In this paper, for the first time, the problem of probabilistic controllability in Causal Bayesian Networks (CBNs) is studied. More specifically, the aim of this paper is two-fold: (i) to introduce and formalize the problem of probabilistic structural controllability in CBNs, and (ii) to identify a sufficient set of driver variables for the purpose of probabilistic structural controllability of a generic CBN. We also elaborate on the nature of minimality the identified set of driver variables satisfies. In this context, the term "structural" signifies the condition wherein solely the structure of the CBN is known.